module module high

`IndisputableMonolith.StandardModel.HiggsEFTBridge`

This module defines the RS Higgs effective potential at canonical mass dimension four as V_RS(Λ, v, h) = Λ⁴ J(exp(h/v)). It bridges recognition cost geometry to the Standard Model Higgs sector within the EFT chain. Physicists deriving SM parameters from the recognition substrate would cite it. The module consists of definitions and lemmas establishing the potential's cosh form, non-negativity, and quartic expansion coefficients.

claim$V_{RS}(Λ, v, h) = Λ^4 J( exp(h/v) )$ where $J(x) = (x + x^{-1})/2 - 1$ is the J-cost function.

background

The module sits inside the Recognition Science framework that derives all physics from one functional equation. It imports the RS time quantum τ₀ from Constants and the J-cost function from the Cost module. The J-cost obeys the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The module introduces the effective potential for the Higgs field h scaled by the vacuum expectation value v at cutoff scale Λ.

proof idea

This is a definition module, no proofs. It supplies a sequence of definitions (V_RS, V_RS_eq_cosh, V_RS_nonneg, quadratic_coefficient, quartic_coefficient_canonical) together with supporting lemmas that establish algebraic identities and bounds on the quartic truncation.

why it matters in Recognition Science

The module supplies the effective scalar coordinate step in the RS cost geometry to canonical Higgs EFT chain. It is imported by the master HiggsEFTLowEnergyLimit module and feeds ElectroweakMassBridge, HiggsObservableSkeleton, and LongitudinalVectorScattering. It realizes the transition from recognition cost geometry to the Standard Model Higgs sector described in the root IndisputableMonolith documentation.

scope and limits

Does not derive the full Standard Model Lagrangian or gauge couplings.
Does not compute numerical Higgs masses or decay widths.
Does not address renormalization group evolution or higher-dimensional operators.
Does not incorporate loop corrections or UV completion details.

used by (5)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith module_import
IndisputableMonolith.StandardModel.ElectroweakMassBridge module_import
IndisputableMonolith.StandardModel.HiggsEFTLowEnergyLimit module_import
IndisputableMonolith.StandardModel.HiggsObservableSkeleton module_import
IndisputableMonolith.StandardModel.LongitudinalVectorScattering module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (18)

def V_RS L67
theorem V_RS_eq_cosh L70
theorem V_RS_at_vacuum L76
theorem V_RS_nonneg L81
def V_RS_quartic L91
theorem exp_sub_trunc6_le L99
theorem cosh_quartic_error L115
theorem jcost_quartic_error L142
theorem V_RS_quartic_error L156
def quadratic_coefficient L176
def quartic_coefficient_canonical L179
theorem V_RS_quartic_canonical L183
def NormalizationHypothesis L201
theorem mass_term_matches_SM L206
theorem quartic_coupling_from_normalization L220
structure HiggsEFTBridgeCert L238
def higgsEFTBridgeCert L262
theorem higgsEFTBridgeCert_inhabited L271